In his latest book, Realistic Rationalism (Cambridge, MA: MIT Press, 1998), Jerrold J. Katz proposes an ontology designed to handle putative counterexamples to the traditional abstract/concrete distinction. Objects like the equator and impure sets, which appear to have both abstract and concrete components, are problematic for classical Platonism, whose exclusive categories of objects with spatiotemporal location and objects lacking spatial or temporal location leave no room for them. Katz proposes to add a “composite” category to Plato’s dualistic ontology, which is supposed to include all those objects with both abstract and concrete components.But every concrete object stands in an indefinite number of relations to abstract ones. Thus, Katz must offer principled criteria describing just those relations that produce a composite object, lest all concrete objects turn out to be composite. The trouble that he has in specifying such a “creative” relationship results from his clinging to the traditional definitions of “abstract” and “concrete.” The substance dualism that results renders the articulation of any relations between abstract and concrete difficult, and a category such as Katz’s “composite objects” impossible